Existence of positive solutions for second-order semipositone differential equations on the half-line

In this paper, by means of constructing a special cone, we obtain a sufficient condition for the existence of positive solution for semipositone singular Sturm-Liouville boundary value problem on the half-line. The results obtained generalize and improve the corresponding results of Zhang and Liu in papers [X.G. Zhang, L.S. Liu, Positive solutions of superlinear semipositone singular Dirichlet boundary value problems, J. Math. Anal. Appl. 316 (2006) 525–537, Y.S. Liu, Existence and unboundedness of positive solutions for singular boundary value problems on half-line, Appl. Math. Comput. 144 (2003) 543–556].